miscon:math.fractions.multiply-mixed-parts-separately · draft · trust low · v0.1.1 · kind procedural-bug

Multiplying mixed numbers part by part

To multiply mixed numbers you multiply the whole numbers together and the fractions together and put the two results back together.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-mixed-parts-separately
UUID
89ca96fb-84d7-4b24-a0f0-c24cf282e25c
Domain
math.fractions
Level band
middle
Locale
en
About
CCSS 5.NF.B.4 http://corestandards.org/Math/Content/5/NF/B/4/

Evidence patterns

Pattern 0: multiply two mixed numbers

product = (whole x whole) and (fraction x fraction) written as a mixed number; the cross terms are dropped

Item2 1/2 x 3 1/3 = ?
Expected8 1/3
Response6 1/6

Discriminators

vs a slip. The answer is too small by exactly the two cross products and the pattern holds across items. A slip is an arithmetic error within the full method.

vs math.fractions.multiply-with-common-denominator. That bug appears on proper-fraction items; this one only appears with mixed numbers.

Relations

conflicts_with
CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction http://corestandards.org/Math/Content/5/NF/B/4/
resolved_by
CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction http://corestandards.org/Math/Content/5/NF/B/4/
confusable_with
math.fractions.multiply-with-common-denominator

Alignments

Provenance

Origin: llm-drafted

  1. Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon.
  2. Newton, K. J. (2008). An extensive analysis of preservice elementary teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. doi:10.3102/0002831208320851
  3. Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge.

Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review.

Review status

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Formats

Cite

miscon:math.fractions.multiply-mixed-parts-separately
https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-mixed-parts-separately